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@ -8,6 +8,8 @@ from __future__ import division
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from wafo.plotbackend import plotbackend
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from wafo.misc import ecross, findcross, JITImport
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from scipy.misc.ppimport import ppimport
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import numdifftools
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from scipy.linalg import pinv2
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@ -16,12 +18,13 @@ from scipy.linalg import pinv2
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from scipy import optimize
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# Trick to avoid error due to circular import
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#_WAFOCOV = ppimport('wafo.covariance')
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_WAFODIST = JITImport('wafo.stats.distributions')
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_WAFODIST = ppimport('wafo.stats.distributions')
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#_WAFODIST = JITImport('wafo.stats.distributions')
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from numpy import alltrue, arange, \
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ravel, ones, sum, \
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zeros, log, sqrt, exp
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from numpy import atleast_1d, any, vectorize, asarray, nan, inf, pi
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ravel, ones, sum, \
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zeros, log, sqrt, exp
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from numpy import atleast_1d, any, asarray, nan, inf, pi, reshape, repeat, product, ndarray
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import numpy
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import numpy as np
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@ -38,13 +41,17 @@ floatinfo = np.finfo(float)
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#arr = atleast_1d
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arr = asarray
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all = alltrue
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def valarray(shape, value=nan, typecode=None):
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"""Return an array of all value.
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"""
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out = reshape(repeat([value], product(shape, axis=0), axis=0), shape)
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if typecode is not None:
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out = out.astype(typecode)
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if not isinstance(out, ndarray):
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out = asarray(out)
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return out
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# Frozen RV class
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class rv_frozen(object):
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@ -80,7 +87,7 @@ class rv_frozen(object):
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def __init__(self, dist, *args, **kwds):
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self.dist = dist
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loc0, scale0 = map(kwds.get, ['loc', 'scale'])
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if isinstance(dist,_WAFODIST.rv_continuous):
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if isinstance(dist, _WAFODIST.rv_continuous):
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args, loc0, scale0 = dist.fix_loc_scale(args, loc0, scale0)
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self.par = args + (loc0, scale0)
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else: # rv_discrete
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@ -88,37 +95,37 @@ class rv_frozen(object):
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self.par = args + (loc0,)
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def pdf(self,x):
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def pdf(self, x):
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''' Probability density function at x of the given RV.'''
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return self.dist.pdf(x,*self.par)
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def cdf(self,x):
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return self.dist.pdf(x, *self.par)
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def cdf(self, x):
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'''Cumulative distribution function at x of the given RV.'''
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return self.dist.cdf(x,*self.par)
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def ppf(self,q):
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return self.dist.cdf(x, *self.par)
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def ppf(self, q):
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'''Percent point function (inverse of cdf) at q of the given RV.'''
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return self.dist.ppf(q,*self.par)
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def isf(self,q):
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return self.dist.ppf(q, *self.par)
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def isf(self, q):
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'''Inverse survival function at q of the given RV.'''
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return self.dist.isf(q,*self.par)
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return self.dist.isf(q, *self.par)
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def rvs(self, size=None):
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'''Random variates of given type.'''
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kwds = dict(size=size)
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return self.dist.rvs(*self.par,**kwds)
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def sf(self,x):
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return self.dist.rvs(*self.par, **kwds)
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def sf(self, x):
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'''Survival function (1-cdf) at x of the given RV.'''
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return self.dist.sf(x,*self.par)
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def stats(self,moments='mv'):
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return self.dist.sf(x, *self.par)
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def stats(self, moments='mv'):
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''' Some statistics of the given RV'''
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kwds = dict(moments=moments)
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return self.dist.stats(*self.par,**kwds)
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def moment(self,n):
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return self.dist.stats(*self.par, **kwds)
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def moment(self, n):
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par1 = self.par[:self.dist.numargs]
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return self.dist.moment(n,*par1)
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return self.dist.moment(n, *par1)
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def entropy(self):
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return self.dist.entropy(*self.par)
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def pmf(self,k):
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def pmf(self, k):
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'''Probability mass function at k of the given RV'''
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return self.dist.pmf(k,*self.par)
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return self.dist.pmf(k, *self.par)
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@ -210,11 +217,11 @@ class Profile(object):
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self.title = 'Profile log'
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self.xlabel = ''
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self.ylabel = ''
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self.i_fixed, self.N, self.alpha, self.pmin,self.pmax,self.x,self.logSF,self.link = map(kwds.get,
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['i','N','alpha','pmin','pmax','x','logSF','link'],
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[0,100,0.05,None,None,None,None,None])
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self.i_fixed, self.N, self.alpha, self.pmin, self.pmax, self.x, self.logSF, self.link = map(kwds.get,
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['i', 'N', 'alpha', 'pmin', 'pmax', 'x', 'logSF', 'link'],
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[0, 100, 0.05, None, None, None, None, None])
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self.ylabel = '%g%s CI' % (100*(1.0-self.alpha), '%')
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self.ylabel = '%g%s CI' % (100 * (1.0 - self.alpha), '%')
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if fit_dist.method.startswith('ml'):
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self.title = self.title + 'likelihood'
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Lmax = fit_dist.LLmax
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@ -223,16 +230,16 @@ class Profile(object):
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Lmax = fit_dist.LPSmax
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else:
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raise ValueError("PROFILE is only valid for ML- or MPS- estimators")
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if fit_dist.par_fix==None:
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isnotfixed = valarray(fit_dist.par.shape,True)
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if fit_dist.par_fix == None:
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isnotfixed = valarray(fit_dist.par.shape, True)
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else:
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isnotfixed = 1-numpy.isfinite(fit_dist.par_fix)
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isnotfixed = 1 - numpy.isfinite(fit_dist.par_fix)
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self.i_notfixed = nonzero(isnotfixed)
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self.i_fixed = atleast_1d(self.i_fixed)
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if 1-isnotfixed[self.i_fixed]:
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if 1 - isnotfixed[self.i_fixed]:
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raise ValueError("Index i must be equal to an index to one of the free parameters.")
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isfree = isnotfixed
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@ -240,9 +247,9 @@ class Profile(object):
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self.i_free = nonzero(isfree)
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self.Lmax = Lmax
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self.alpha_Lrange = 0.5*chi2.isf(self.alpha,1)
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self.alpha_Lrange = 0.5 * _WAFODIST.chi2.isf(self.alpha, 1)
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self.alpha_cross_level = Lmax - self.alpha_Lrange
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lowLevel = self.alpha_cross_level-self.alpha_Lrange/7.0
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lowLevel = self.alpha_cross_level - self.alpha_Lrange / 7.0
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## Check that par are actually at the optimum
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phatv = fit_dist.par.copy()
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@ -252,26 +259,26 @@ class Profile(object):
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## Set up variable to profile and _local_link function
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self.profile_x = not self.x==None
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self.profile_logSF = not (self.logSF==None or self.profile_x)
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self.profile_x = not self.x == None
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self.profile_logSF = not (self.logSF == None or self.profile_x)
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self.profile_par = not (self.profile_x or self.profile_logSF)
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if self.link==None:
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if self.link == None:
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self.link = self.fit_dist.dist.link
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if self.profile_par:
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self._local_link = lambda fix_par, par : fix_par
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self.xlabel = 'phat(%d)'% self.i_fixed
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self.xlabel = 'phat(%d)' % self.i_fixed
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p_opt = self._par[self.i_fixed]
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elif self.profile_x:
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self.logSF = log(fit_dist.sf(self.x))
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self._local_link = lambda fix_par, par : self.link(fix_par,self.logSF,par,self.i_fixed)
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self._local_link = lambda fix_par, par : self.link(fix_par, self.logSF, par, self.i_fixed)
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self.xlabel = 'x'
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p_opt = self.x
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elif self.profile_logSF:
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p_opt = self.logSF
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self.x = fit_dist.isf(exp(p_opt))
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self._local_link = lambda fix_par, par : self.link(self.x,fix_par,par,self.i_fixed)
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self.xlabel= 'log(R)'
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self._local_link = lambda fix_par, par : self.link(self.x, fix_par, par, self.i_fixed)
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self.xlabel = 'log(R)'
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else:
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raise ValueError("You must supply a non-empty quantile (x) or probability (logSF) in order to profile it!")
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@ -283,47 +290,47 @@ class Profile(object):
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mylogfun = self._nlogfun
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self.data = numpy.empty_like(pvec)
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self.data[:] = nan
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k1 = (pvec>=p_opt).argmax()
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for ix in xrange(k1,-1,-1):
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phatfree = optimize.fmin(mylogfun,phatfree,args =(pvec[ix],) ,disp=0)
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self.data[ix] = -mylogfun(phatfree,pvec[ix])
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if self.data[ix]<self.alpha_cross_level:
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k1 = (pvec >= p_opt).argmax()
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for ix in xrange(k1, -1, -1):
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phatfree = optimize.fmin(mylogfun, phatfree, args=(pvec[ix],) , disp=0)
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self.data[ix] = -mylogfun(phatfree, pvec[ix])
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if self.data[ix] < self.alpha_cross_level:
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pvec[:ix] = nan
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break
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phatfree = phatv[self.i_free].copy()
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for ix in xrange(k1+1,pvec.size):
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phatfree = optimize.fmin(mylogfun,phatfree,args =(pvec[ix],) ,disp=0)
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self.data[ix] = -mylogfun(phatfree,pvec[ix])
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if self.data[ix]<self.alpha_cross_level:
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pvec[ix+1:] = nan
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for ix in xrange(k1 + 1, pvec.size):
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phatfree = optimize.fmin(mylogfun, phatfree, args=(pvec[ix],) , disp=0)
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self.data[ix] = -mylogfun(phatfree, pvec[ix])
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if self.data[ix] < self.alpha_cross_level:
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pvec[ix + 1:] = nan
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break
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# prettify result
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ix = nonzero(numpy.isfinite(pvec))
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self.data = self.data[ix]
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self.args = pvec[ix]
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cond =self.data==-numpy.inf
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cond = self.data == -numpy.inf
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if any(cond):
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ind, = cond.nonzero()
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self.data.put(ind, numpy.finfo(float).min/2.0)
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ind1 = numpy.where(ind==0,ind,ind-1)
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cl = self.alpha_cross_level-self.alpha_Lrange/2.0
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t0 = ecross(self.args,self.data,ind1,cl)
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self.data.put(ind, numpy.finfo(float).min / 2.0)
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ind1 = numpy.where(ind == 0, ind, ind - 1)
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cl = self.alpha_cross_level - self.alpha_Lrange / 2.0
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t0 = ecross(self.args, self.data, ind1, cl)
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self.data.put(ind,cl)
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self.args.put(ind,t0)
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self.data.put(ind, cl)
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self.args.put(ind, t0)
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def _get_pvec(self,p_opt):
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def _get_pvec(self, p_opt):
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''' return proper interval for the variable to profile
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'''
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linspace = numpy.linspace
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if self.pmin==None or self.pmax==None:
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if self.pmin == None or self.pmax == None:
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if self.profile_par:
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pvar = self.fit_dist.par_cov[self.i_fixed,:][:,self.i_fixed]
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pvar = self.fit_dist.par_cov[self.i_fixed, :][:, self.i_fixed]
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else:
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i_notfixed = self.i_notfixed
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phatv = self._par
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@ -334,38 +341,38 @@ class Profile(object):
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gradfun = numdifftools.Gradient(self._myprbfun)
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drl = gradfun(phatv[self.i_notfixed])
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pcov = self.fit_dist.par_cov[i_notfixed,:][:,i_notfixed]
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pvar = sum(numpy.dot(drl,pcov)*drl)
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pcov = self.fit_dist.par_cov[i_notfixed, :][:, i_notfixed]
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pvar = sum(numpy.dot(drl, pcov) * drl)
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p_crit = norm.isf(self.alpha/2.0)*sqrt(numpy.ravel(pvar))*1.5
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if self.pmin==None:
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self.pmin = p_opt-5.0*p_crit
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if self.pmax==None:
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self.pmax = p_opt+5.0*p_crit
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p_crit = _WAFODIST.norm.isf(self.alpha / 2.0) * sqrt(numpy.ravel(pvar)) * 1.5
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if self.pmin == None:
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self.pmin = p_opt - 5.0 * p_crit
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if self.pmax == None:
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|
|
self.pmax = p_opt + 5.0 * p_crit
|
|
|
|
|
|
|
|
|
|
N4 = numpy.floor(self.N/4.0)
|
|
|
|
|
N4 = numpy.floor(self.N / 4.0)
|
|
|
|
|
|
|
|
|
|
pvec1 = linspace(self.pmin,p_opt-p_crit,N4+1)
|
|
|
|
|
pvec2 = linspace(p_opt-p_crit,p_opt+p_crit,self.N-2*N4)
|
|
|
|
|
pvec3 = linspace(p_opt+p_crit,self.pmax,N4+1)
|
|
|
|
|
pvec = numpy.unique(numpy.hstack((pvec1,p_opt,pvec2,pvec3)))
|
|
|
|
|
pvec1 = linspace(self.pmin, p_opt - p_crit, N4 + 1)
|
|
|
|
|
pvec2 = linspace(p_opt - p_crit, p_opt + p_crit, self.N - 2 * N4)
|
|
|
|
|
pvec3 = linspace(p_opt + p_crit, self.pmax, N4 + 1)
|
|
|
|
|
pvec = numpy.unique(numpy.hstack((pvec1, p_opt, pvec2, pvec3)))
|
|
|
|
|
|
|
|
|
|
else:
|
|
|
|
|
pvec = linspace(self.pmin,self.pmax,self.N)
|
|
|
|
|
pvec = linspace(self.pmin, self.pmax, self.N)
|
|
|
|
|
return pvec
|
|
|
|
|
def _myinvfun(self,phatnotfixed):
|
|
|
|
|
def _myinvfun(self, phatnotfixed):
|
|
|
|
|
mphat = self._par.copy()
|
|
|
|
|
mphat[self.i_notfixed] = phatnotfixed;
|
|
|
|
|
prb = exp(self.logSF)
|
|
|
|
|
return self.fit_dist.dist.isf(prb,*mphat);
|
|
|
|
|
return self.fit_dist.dist.isf(prb, *mphat);
|
|
|
|
|
|
|
|
|
|
def _myprbfun(phatnotfixed):
|
|
|
|
|
def _myprbfun(self, phatnotfixed):
|
|
|
|
|
mphat = self._par.copy()
|
|
|
|
|
mphat[self.i_notfixed] = phatnotfixed;
|
|
|
|
|
return self.fit_dist.dist.sf(self.x,*mphat);
|
|
|
|
|
return self.fit_dist.dist.sf(self.x, *mphat)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def _nlogfun(self,free_par,fix_par):
|
|
|
|
|
def _nlogfun(self, free_par, fix_par):
|
|
|
|
|
''' Return negative of loglike or logps function
|
|
|
|
|
|
|
|
|
|
free_par - vector of free parameters
|
|
|
|
|
@ -376,45 +383,45 @@ class Profile(object):
|
|
|
|
|
par = self._par
|
|
|
|
|
par[self.i_free] = free_par
|
|
|
|
|
# _local_link: connects fixed quantile or probability with fixed distribution parameter
|
|
|
|
|
par[self.i_fixed] = self._local_link(fix_par,par)
|
|
|
|
|
par[self.i_fixed] = self._local_link(fix_par, par)
|
|
|
|
|
return self.fit_dist.fitfun(par)
|
|
|
|
|
|
|
|
|
|
def get_CI(self,alpha=0.05):
|
|
|
|
|
def get_CI(self, alpha=0.05):
|
|
|
|
|
'''Return confidence interval
|
|
|
|
|
'''
|
|
|
|
|
if alpha<self.alpha:
|
|
|
|
|
if alpha < self.alpha:
|
|
|
|
|
raise ValueError('Unable to return CI with alpha less than %g' % self.alpha)
|
|
|
|
|
|
|
|
|
|
cross_level = self.Lmax - 0.5*chi2.isf(alpha,1)
|
|
|
|
|
ind = findcross(self.data,cross_level)
|
|
|
|
|
cross_level = self.Lmax - 0.5 * _WAFODIST.chi2.isf(alpha, 1)
|
|
|
|
|
ind = findcross(self.data, cross_level)
|
|
|
|
|
N = len(ind)
|
|
|
|
|
if N==0:
|
|
|
|
|
if N == 0:
|
|
|
|
|
#Warning('upper bound for XXX is larger'
|
|
|
|
|
#Warning('lower bound for XXX is smaller'
|
|
|
|
|
CI = (self.pmin,self.pmax)
|
|
|
|
|
elif N==1:
|
|
|
|
|
x0 = ecross(self.args,self.data,ind,cross_level)
|
|
|
|
|
isUpcrossing = self.data[ind]>self.data[ind+1]
|
|
|
|
|
CI = (self.pmin, self.pmax)
|
|
|
|
|
elif N == 1:
|
|
|
|
|
x0 = ecross(self.args, self.data, ind, cross_level)
|
|
|
|
|
isUpcrossing = self.data[ind] > self.data[ind + 1]
|
|
|
|
|
if isUpcrossing:
|
|
|
|
|
CI = (x0,self.pmax)
|
|
|
|
|
CI = (x0, self.pmax)
|
|
|
|
|
#Warning('upper bound for XXX is larger'
|
|
|
|
|
else:
|
|
|
|
|
CI = (self.pmin,x0)
|
|
|
|
|
CI = (self.pmin, x0)
|
|
|
|
|
#Warning('lower bound for XXX is smaller'
|
|
|
|
|
|
|
|
|
|
elif N==2:
|
|
|
|
|
CI = ecross(self.args,self.data,ind,cross_level)
|
|
|
|
|
elif N == 2:
|
|
|
|
|
CI = ecross(self.args, self.data, ind, cross_level)
|
|
|
|
|
else:
|
|
|
|
|
# Warning('Number of crossings too large!')
|
|
|
|
|
CI = ecross(self.args,self.data,ind[[0,-1]],cross_level)
|
|
|
|
|
CI = ecross(self.args, self.data, ind[[0, -1]], cross_level)
|
|
|
|
|
return CI
|
|
|
|
|
|
|
|
|
|
def plot(self):
|
|
|
|
|
''' Plot profile function with 100(1-alpha)% CI
|
|
|
|
|
'''
|
|
|
|
|
plotbackend.plot(self.args,self.data,
|
|
|
|
|
self.args[[0,-1]],[self.Lmax,]*2,'r',
|
|
|
|
|
self.args[[0,-1]],[self.alpha_cross_level,]*2,'r')
|
|
|
|
|
plotbackend.plot(self.args, self.data,
|
|
|
|
|
self.args[[0, -1]], [self.Lmax, ]*2, 'r',
|
|
|
|
|
self.args[[0, -1]], [self.alpha_cross_level, ]*2, 'r')
|
|
|
|
|
plotbackend.title(self.title)
|
|
|
|
|
plotbackend.ylabel(self.ylabel)
|
|
|
|
|
plotbackend.xlabel(self.xlabel)
|
|
|
|
|
@ -454,7 +461,7 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
self.dist = dist
|
|
|
|
|
numargs = dist.numargs
|
|
|
|
|
|
|
|
|
|
self.method, self.alpha, self.par_fix, self.search, self.copydata= map(kwds.get,['method','alpha','par_fix','search','copydata'],['ml',0.05,None,True,True])
|
|
|
|
|
self.method, self.alpha, self.par_fix, self.search, self.copydata = map(kwds.get, ['method', 'alpha', 'par_fix', 'search', 'copydata'], ['ml', 0.05, None, True, True])
|
|
|
|
|
self.data = ravel(data)
|
|
|
|
|
if self.copydata:
|
|
|
|
|
self.data = self.data.copy()
|
|
|
|
|
@ -464,20 +471,20 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
else:
|
|
|
|
|
self._fitfun = dist.nnlf
|
|
|
|
|
|
|
|
|
|
allfixed = False
|
|
|
|
|
allfixed = False
|
|
|
|
|
isfinite = numpy.isfinite
|
|
|
|
|
somefixed = (self.par_fix !=None) and any(isfinite(self.par_fix))
|
|
|
|
|
somefixed = (self.par_fix != None) and any(isfinite(self.par_fix))
|
|
|
|
|
|
|
|
|
|
if somefixed:
|
|
|
|
|
fitfun = self._fxfitfun
|
|
|
|
|
self.par_fix = tuple(self.par_fix)
|
|
|
|
|
allfixed = all(isfinite(self.par_fix))
|
|
|
|
|
self.par = atleast_1d(self.par_fix)
|
|
|
|
|
self.i_notfixed = nonzero(1-isfinite(self.par))
|
|
|
|
|
self.i_fixed = nonzero(isfinite(self.par))
|
|
|
|
|
if len(self.par) != numargs+2:
|
|
|
|
|
self.i_notfixed = nonzero(1 - isfinite(self.par))
|
|
|
|
|
self.i_fixed = nonzero(isfinite(self.par))
|
|
|
|
|
if len(self.par) != numargs + 2:
|
|
|
|
|
raise ValueError, "Wrong number of input arguments."
|
|
|
|
|
if len(args)!=len(self.i_notfixed):
|
|
|
|
|
if len(args) != len(self.i_notfixed):
|
|
|
|
|
raise ValueError("Length of args must equal number of non-fixed parameters given in par_fix! (%d) " % len(self.i_notfixed))
|
|
|
|
|
x0 = atleast_1d(args)
|
|
|
|
|
else:
|
|
|
|
|
@ -489,7 +496,7 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
if Narg > numargs:
|
|
|
|
|
raise ValueError, "Too many input arguments."
|
|
|
|
|
else:
|
|
|
|
|
args += (1.0,)*(numargs-Narg)
|
|
|
|
|
args += (1.0,)*(numargs - Narg)
|
|
|
|
|
# location and scale are at the end
|
|
|
|
|
x0 = args + (loc0, scale0)
|
|
|
|
|
x0 = atleast_1d(x0)
|
|
|
|
|
@ -497,7 +504,7 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
numpar = len(x0)
|
|
|
|
|
if self.search and not allfixed:
|
|
|
|
|
#args=(self.data,),
|
|
|
|
|
par = optimize.fmin(fitfun,x0,disp=0)
|
|
|
|
|
par = optimize.fmin(fitfun, x0, disp=0)
|
|
|
|
|
if not somefixed:
|
|
|
|
|
self.par = par
|
|
|
|
|
elif (not allfixed) and somefixed:
|
|
|
|
|
@ -505,43 +512,43 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
else:
|
|
|
|
|
self.par = x0
|
|
|
|
|
|
|
|
|
|
np = numargs+2
|
|
|
|
|
np = numargs + 2
|
|
|
|
|
|
|
|
|
|
self.par_upper = None
|
|
|
|
|
self.par_lower = None
|
|
|
|
|
self.par_cov = zeros((np,np))
|
|
|
|
|
self.LLmax = -dist.nnlf(self.par,self.data)
|
|
|
|
|
self.LPSmax = -dist.nlogps(self.par,self.data)
|
|
|
|
|
self.pvalue = dist.pvalue(self.par,self.data,unknown_numpar=numpar)
|
|
|
|
|
H = numpy.asmatrix(dist.hessian_nnlf(self.par,self.data))
|
|
|
|
|
self.par_cov = zeros((np, np))
|
|
|
|
|
self.LLmax = -dist.nnlf(self.par, self.data)
|
|
|
|
|
self.LPSmax = -dist.nlogps(self.par, self.data)
|
|
|
|
|
self.pvalue = dist.pvalue(self.par, self.data, unknown_numpar=numpar)
|
|
|
|
|
H = numpy.asmatrix(dist.hessian_nnlf(self.par, self.data))
|
|
|
|
|
self.H = H
|
|
|
|
|
try:
|
|
|
|
|
if allfixed:
|
|
|
|
|
pass
|
|
|
|
|
elif somefixed:
|
|
|
|
|
pcov = -pinv2(H[self.i_notfixed,:][...,self.i_notfixed])
|
|
|
|
|
for row,ix in enumerate(list(self.i_notfixed)):
|
|
|
|
|
self.par_cov[ix,self.i_notfixed] = pcov[row,:]
|
|
|
|
|
pcov = -pinv2(H[self.i_notfixed, :][..., self.i_notfixed])
|
|
|
|
|
for row, ix in enumerate(list(self.i_notfixed)):
|
|
|
|
|
self.par_cov[ix, self.i_notfixed] = pcov[row, :]
|
|
|
|
|
|
|
|
|
|
else:
|
|
|
|
|
self.par_cov = -pinv2(H)
|
|
|
|
|
except:
|
|
|
|
|
self.par_cov[:,:] = nan
|
|
|
|
|
self.par_cov[:, :] = nan
|
|
|
|
|
|
|
|
|
|
pvar = numpy.diag(self.par_cov)
|
|
|
|
|
zcrit = -norm.ppf(self.alpha/2.0)
|
|
|
|
|
self.par_lower = self.par-zcrit*sqrt(pvar)
|
|
|
|
|
self.par_upper = self.par+zcrit*sqrt(pvar)
|
|
|
|
|
zcrit = -_WAFODIST.norm.ppf(self.alpha / 2.0)
|
|
|
|
|
self.par_lower = self.par - zcrit * sqrt(pvar)
|
|
|
|
|
self.par_upper = self.par + zcrit * sqrt(pvar)
|
|
|
|
|
|
|
|
|
|
def fitfun(self,phat):
|
|
|
|
|
return self._fitfun(phat,self.data)
|
|
|
|
|
def fitfun(self, phat):
|
|
|
|
|
return self._fitfun(phat, self.data)
|
|
|
|
|
|
|
|
|
|
def _fxfitfun(self,phat10):
|
|
|
|
|
def _fxfitfun(self, phat10):
|
|
|
|
|
self.par[self.i_notfixed] = phat10
|
|
|
|
|
return self._fitfun(self.par,self.data)
|
|
|
|
|
return self._fitfun(self.par, self.data)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
def profile(self,**kwds):
|
|
|
|
|
def profile(self, **kwds):
|
|
|
|
|
''' Profile Log- likelihood or Log Product Spacing- function,
|
|
|
|
|
which can be used for constructing confidence interval for
|
|
|
|
|
either phat(i), probability or quantile.
|
|
|
|
|
@ -609,12 +616,10 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
--------
|
|
|
|
|
Profile
|
|
|
|
|
'''
|
|
|
|
|
if not self.par_fix==None:
|
|
|
|
|
i1 = kwds.setdefault('i',(1-numpy.isfinite(self.par_fix)).argmax())
|
|
|
|
|
|
|
|
|
|
return Profile(self,**kwds)
|
|
|
|
|
|
|
|
|
|
if not self.par_fix == None:
|
|
|
|
|
i1 = kwds.setdefault('i', (1 - numpy.isfinite(self.par_fix)).argmax())
|
|
|
|
|
|
|
|
|
|
return Profile(self, **kwds)
|
|
|
|
|
|
|
|
|
|
def plotfitsumry(self):
|
|
|
|
|
''' Plot various diagnostic plots to asses the quality of the fit.
|
|
|
|
|
@ -626,31 +631,31 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
should follow the model and the residual plots will be linear. Other
|
|
|
|
|
distribution types will introduce curvature in the residual plots.
|
|
|
|
|
'''
|
|
|
|
|
plotbackend.subplot(2,2,1)
|
|
|
|
|
plotbackend.subplot(2, 2, 1)
|
|
|
|
|
#self.plotecdf()
|
|
|
|
|
self.plotesf()
|
|
|
|
|
plotbackend.subplot(2,2,2)
|
|
|
|
|
plotbackend.subplot(2, 2, 2)
|
|
|
|
|
self.plotepdf()
|
|
|
|
|
plotbackend.subplot(2,2,3)
|
|
|
|
|
plotbackend.subplot(2, 2, 3)
|
|
|
|
|
self.plotresprb()
|
|
|
|
|
plotbackend.subplot(2,2,4)
|
|
|
|
|
plotbackend.subplot(2, 2, 4)
|
|
|
|
|
self.plotresq()
|
|
|
|
|
fixstr = ''
|
|
|
|
|
if not self.par_fix==None:
|
|
|
|
|
if not self.par_fix == None:
|
|
|
|
|
numfix = len(self.i_fixed)
|
|
|
|
|
if numfix>0:
|
|
|
|
|
if numfix > 0:
|
|
|
|
|
format = '%d,'*numfix
|
|
|
|
|
format = format[:-1]
|
|
|
|
|
format1 = '%g,'*numfix
|
|
|
|
|
format1 = format1[:-1]
|
|
|
|
|
phatistr = format % tuple(self.i_fixed)
|
|
|
|
|
phatvstr = format1 % tuple(self.par[self.i_fixed])
|
|
|
|
|
fixstr = 'Fixed: phat[%s] = %s ' % (phatistr,phatvstr)
|
|
|
|
|
fixstr = 'Fixed: phat[%s] = %s ' % (phatistr, phatvstr)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
infostr = 'Fit method: %s, Fit p-value: %2.2f %s' % (self.method,self.pvalue,fixstr)
|
|
|
|
|
infostr = 'Fit method: %s, Fit p-value: %2.2f %s' % (self.method, self.pvalue, fixstr)
|
|
|
|
|
try:
|
|
|
|
|
plotbackend.figtext(0.05,0.01,infostr)
|
|
|
|
|
plotbackend.figtext(0.05, 0.01, infostr)
|
|
|
|
|
except:
|
|
|
|
|
pass
|
|
|
|
|
|
|
|
|
|
@ -663,8 +668,8 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
Other distribution types will introduce deviations in the plot.
|
|
|
|
|
'''
|
|
|
|
|
n = len(self.data)
|
|
|
|
|
SF = (arange(n,0,-1))/n
|
|
|
|
|
plotbackend.semilogy(self.data,SF,'b.',self.data,self.sf(self.data),'r-')
|
|
|
|
|
SF = (arange(n, 0, -1)) / n
|
|
|
|
|
plotbackend.semilogy(self.data, SF, 'b.', self.data, self.sf(self.data), 'r-')
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#plotbackend.plot(self.data,SF,'b.',self.data,self.sf(self.data),'r-')
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plotbackend.xlabel('x');
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@ -680,8 +685,8 @@ class FitDistribution(rv_frozen):
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|
Other distribution types will introduce deviations in the plot.
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|
'''
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|
n = len(self.data)
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F = (arange(1,n+1))/n
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plotbackend.plot(self.data,F,'b.',self.data,self.cdf(self.data),'r-')
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F = (arange(1, n + 1)) / n
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plotbackend.plot(self.data, F, 'b.', self.data, self.cdf(self.data), 'r-')
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plotbackend.xlabel('x');
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@ -697,20 +702,20 @@ class FitDistribution(rv_frozen):
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|
Other distribution types will introduce deviations in the plot.
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|
'''
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bin,limits = numpy.histogram(self.data,normed=True,new=True)
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limits.shape = (-1,1)
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xx = limits.repeat(3,axis=1)
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bin, limits = numpy.histogram(self.data, normed=True, new=True)
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limits.shape = (-1, 1)
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xx = limits.repeat(3, axis=1)
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xx.shape = (-1,)
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xx = xx[1:-1]
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bin.shape = (-1,1)
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yy = bin.repeat(3,axis=1)
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bin.shape = (-1, 1)
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yy = bin.repeat(3, axis=1)
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#yy[0,0] = 0.0 # pdf
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yy[:,0] = 0.0 # histogram
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yy[:, 0] = 0.0 # histogram
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yy.shape = (-1,)
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yy = numpy.hstack((yy,0.0))
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yy = numpy.hstack((yy, 0.0))
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#plotbackend.hist(self.data,normed=True,fill=False)
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plotbackend.plot(self.data,self.pdf(self.data),'r-',xx,yy,'b-')
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plotbackend.plot(self.data, self.pdf(self.data), 'r-', xx, yy, 'b-')
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plotbackend.xlabel('x');
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plotbackend.ylabel('f(x) (%s)' % self.dist.name)
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@ -725,11 +730,11 @@ class FitDistribution(rv_frozen):
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|
plot will be linear. Other distribution types will introduce
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|
curvature in the plot.
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|
'''
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|
n=len(self.data)
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|
eprob = (arange(1,n+1)-0.5)/n
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n = len(self.data)
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|
eprob = (arange(1, n + 1) - 0.5) / n
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|
y = self.ppf(eprob)
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|
y1 = self.data[[0,-1]]
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|
plotbackend.plot(self.data,y,'b.',y1,y1,'r-')
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|
y1 = self.data[[0, -1]]
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|
plotbackend.plot(self.data, y, 'b.', y1, y1, 'r-')
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plotbackend.xlabel('Empirical')
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|
plotbackend.ylabel('Model (%s)' % self.dist.name)
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|
@ -747,10 +752,10 @@ class FitDistribution(rv_frozen):
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|
'''
|
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|
|
n = len(self.data);
|
|
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|
|
#ecdf = (0.5:n-0.5)/n;
|
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|
|
ecdf = arange(1,n+1)/(n+1)
|
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|
|
ecdf = arange(1, n + 1) / (n + 1)
|
|
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|
|
mcdf = self.cdf(self.data)
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|
|
p1 = [0,1]
|
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|
|
plotbackend.plot(ecdf,mcdf,'b.',p1,p1,'r-')
|
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|
|
p1 = [0, 1]
|
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|
|
plotbackend.plot(ecdf, mcdf, 'b.', p1, p1, 'r-')
|
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|
|
plotbackend.xlabel('Empirical')
|
|
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|
|
@ -761,37 +766,37 @@ class FitDistribution(rv_frozen):
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|
|
def pvalue(self,theta,x,unknown_numpar=None):
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|
|
def pvalue(self, theta, x, unknown_numpar=None):
|
|
|
|
|
''' Return the P-value for the fit using Moran's negative log Product Spacings statistic
|
|
|
|
|
|
|
|
|
|
where theta are the parameters (including loc and scale)
|
|
|
|
|
|
|
|
|
|
Note: the data in x must be sorted
|
|
|
|
|
'''
|
|
|
|
|
dx = numpy.diff(x,axis=0)
|
|
|
|
|
tie = (dx==0)
|
|
|
|
|
dx = numpy.diff(x, axis=0)
|
|
|
|
|
tie = (dx == 0)
|
|
|
|
|
if any(tie):
|
|
|
|
|
disp('P-value is on the conservative side (i.e. too large) due to ties in the data!')
|
|
|
|
|
print('P-value is on the conservative side (i.e. too large) due to ties in the data!')
|
|
|
|
|
|
|
|
|
|
T = self.nlogps(theta,x)
|
|
|
|
|
T = self.nlogps(theta, x)
|
|
|
|
|
|
|
|
|
|
n = len(x)
|
|
|
|
|
np1 = n+1
|
|
|
|
|
if unknown_numpar==None:
|
|
|
|
|
np1 = n + 1
|
|
|
|
|
if unknown_numpar == None:
|
|
|
|
|
k = len(theta)
|
|
|
|
|
else:
|
|
|
|
|
k = unknown_numpar
|
|
|
|
|
|
|
|
|
|
isParUnKnown = True
|
|
|
|
|
m = (np1)*(log(np1)+0.57722)-0.5-1.0/(12.*(np1))
|
|
|
|
|
v = (np1)*(pi**2./6.0-1.0)-0.5-1.0/(6.*(np1))
|
|
|
|
|
C1 = m-sqrt(0.5*n*v)
|
|
|
|
|
C2 = sqrt(v/(2.0*n))
|
|
|
|
|
Tn = (T + 0.5*k*isParUnKnown-C1)/C2 # chi2 with n degrees of freedom
|
|
|
|
|
pvalue = chi2.sf(Tn,n)
|
|
|
|
|
m = (np1) * (log(np1) + 0.57722) - 0.5 - 1.0 / (12. * (np1))
|
|
|
|
|
v = (np1) * (pi ** 2. / 6.0 - 1.0) - 0.5 - 1.0 / (6. * (np1))
|
|
|
|
|
C1 = m - sqrt(0.5 * n * v)
|
|
|
|
|
C2 = sqrt(v / (2.0 * n))
|
|
|
|
|
Tn = (T + 0.5 * k * isParUnKnown - C1) / C2 # chi2 with n degrees of freedom
|
|
|
|
|
pvalue = _WAFODIST.chi2.sf(Tn, n)
|
|
|
|
|
return pvalue
|
|
|
|
|
|
|
|
|
|
def nlogps(self,theta,x):
|
|
|
|
|
def nlogps(self, theta, x):
|
|
|
|
|
""" Moran's negative log Product Spacings statistic
|
|
|
|
|
|
|
|
|
|
where theta are the parameters (including loc and scale)
|
|
|
|
|
@ -825,25 +830,25 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
raise ValueError, "Not enough input arguments."
|
|
|
|
|
if not self.dist._argcheck(*args) or scale <= 0:
|
|
|
|
|
return inf
|
|
|
|
|
x = arr((x-loc) / scale)
|
|
|
|
|
x = arr((x - loc) / scale)
|
|
|
|
|
cond0 = (x <= self.dist.a) | (x >= self.dist.b)
|
|
|
|
|
if (any(cond0)):
|
|
|
|
|
return inf
|
|
|
|
|
else:
|
|
|
|
|
linfo = numpy.finfo(float)
|
|
|
|
|
#linfo = numpy.finfo(float)
|
|
|
|
|
realmax = floatinfo.machar.xmax
|
|
|
|
|
|
|
|
|
|
lowertail = True
|
|
|
|
|
if lowertail:
|
|
|
|
|
prb = numpy.hstack((0.0, self.dist.cdf(x,*args), 1.0))
|
|
|
|
|
prb = numpy.hstack((0.0, self.dist.cdf(x, *args), 1.0))
|
|
|
|
|
dprb = numpy.diff(prb)
|
|
|
|
|
else:
|
|
|
|
|
prb = numpy.hstack((1.0, self.dist.sf(x,*args), 0.0))
|
|
|
|
|
prb = numpy.hstack((1.0, self.dist.sf(x, *args), 0.0))
|
|
|
|
|
dprb = -numpy.diff(prb)
|
|
|
|
|
|
|
|
|
|
logD = log(dprb)
|
|
|
|
|
dx = numpy.diff(x,axis=0)
|
|
|
|
|
tie = (dx==0)
|
|
|
|
|
dx = numpy.diff(x, axis=0)
|
|
|
|
|
tie = (dx == 0)
|
|
|
|
|
if any(tie):
|
|
|
|
|
# TODO % implement this method for treating ties in data:
|
|
|
|
|
# Assume measuring error is delta. Then compute
|
|
|
|
|
@ -857,18 +862,18 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
i_tie = nonzero(tie)
|
|
|
|
|
tiedata = x[i_tie]
|
|
|
|
|
|
|
|
|
|
logD[(I_tie[0]+1,)]= log(self.dist._pdf(tiedata,*args)) + log(scale)
|
|
|
|
|
logD[(i_tie[0] + 1,)] = log(self.dist._pdf(tiedata, *args)) + log(scale)
|
|
|
|
|
|
|
|
|
|
finiteD = numpy.isfinite(logD)
|
|
|
|
|
nonfiniteD = 1-finiteD
|
|
|
|
|
nonfiniteD = 1 - finiteD
|
|
|
|
|
if any(nonfiniteD):
|
|
|
|
|
T = -sum(logD[finiteD],axis=0) + 100.0*log(realmax)*sum(nonfiniteD,axis=0);
|
|
|
|
|
T = -sum(logD[finiteD], axis=0) + 100.0 * log(realmax) * sum(nonfiniteD, axis=0);
|
|
|
|
|
else:
|
|
|
|
|
T = -sum(logD,axis=0) #%Moran's negative log product spacing statistic
|
|
|
|
|
T = -sum(logD, axis=0) #%Moran's negative log product spacing statistic
|
|
|
|
|
return T
|
|
|
|
|
|
|
|
|
|
def _nnlf(self, x, *args):
|
|
|
|
|
return -sum(log(self._pdf(x, *args)),axis=0)
|
|
|
|
|
return - sum(log(self._pdf(x, *args)), axis=0)
|
|
|
|
|
|
|
|
|
|
def nnlf(self, theta, x):
|
|
|
|
|
''' Return negative loglikelihood function, i.e., - sum (log pdf(x, theta),axis=0)
|
|
|
|
|
@ -882,23 +887,24 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
raise ValueError, "Not enough input arguments."
|
|
|
|
|
if not self._argcheck(*args) or scale <= 0:
|
|
|
|
|
return inf
|
|
|
|
|
x = arr((x-loc) / scale)
|
|
|
|
|
cond0 = (x<=self.a) | (self.b<=x)
|
|
|
|
|
newCall = False
|
|
|
|
|
if newCall:
|
|
|
|
|
goodargs = argsreduce(1-cond0, *((x,)))
|
|
|
|
|
goodargs = tuple(goodargs + list(args))
|
|
|
|
|
N = len(x)
|
|
|
|
|
Nbad = sum(cond0)
|
|
|
|
|
xmin = floatinfo.machar.xmin
|
|
|
|
|
return self._nnlf(*goodargs) + N*log(scale) + Nbad*100.0*log(xmin)
|
|
|
|
|
elif (any(cond0)):
|
|
|
|
|
x = arr((x - loc) / scale)
|
|
|
|
|
cond0 = (x <= self.a) | (self.b <= x)
|
|
|
|
|
# newCall = False
|
|
|
|
|
# if newCall:
|
|
|
|
|
# goodargs = argsreduce(1-cond0, *((x,)))
|
|
|
|
|
# goodargs = tuple(goodargs + list(args))
|
|
|
|
|
# N = len(x)
|
|
|
|
|
# Nbad = sum(cond0)
|
|
|
|
|
# xmin = floatinfo.machar.xmin
|
|
|
|
|
# return self._nnlf(*goodargs) + N*log(scale) + Nbad*100.0*log(xmin)
|
|
|
|
|
# el
|
|
|
|
|
if (any(cond0)):
|
|
|
|
|
return inf
|
|
|
|
|
else:
|
|
|
|
|
N = len(x)
|
|
|
|
|
return self._nnlf(x, *args) + N*log(scale)
|
|
|
|
|
return self._nnlf(x, *args) + N * log(scale)
|
|
|
|
|
|
|
|
|
|
def hessian_nnlf(self,theta,data,eps=None):
|
|
|
|
|
def hessian_nnlf(self, theta, data, eps=None):
|
|
|
|
|
''' approximate hessian of nnlf where theta are the parameters (including loc and scale)
|
|
|
|
|
'''
|
|
|
|
|
#Nd = len(x)
|
|
|
|
|
@ -908,96 +914,100 @@ class FitDistribution(rv_frozen):
|
|
|
|
|
# This is important when calculating numerical derivatives and is
|
|
|
|
|
# accomplished by the following.
|
|
|
|
|
|
|
|
|
|
if eps==None:
|
|
|
|
|
eps = (floatinfo.machar.eps)**0.4
|
|
|
|
|
if eps == None:
|
|
|
|
|
eps = (floatinfo.machar.eps) ** 0.4
|
|
|
|
|
xmin = floatinfo.machar.xmin
|
|
|
|
|
#myfun = lambda y: max(y,100.0*log(xmin)) #% trick to avoid log of zero
|
|
|
|
|
delta = (eps+2.0)-2.0
|
|
|
|
|
delta2 = delta**2.0
|
|
|
|
|
delta = (eps + 2.0) - 2.0
|
|
|
|
|
delta2 = delta ** 2.0
|
|
|
|
|
# % Approximate 1/(nE( (d L(x|theta)/dtheta)^2)) with
|
|
|
|
|
# % 1/(d^2 L(theta|x)/dtheta^2)
|
|
|
|
|
# % using central differences
|
|
|
|
|
|
|
|
|
|
LL = self.nnlf(theta,data)
|
|
|
|
|
H = zeros((np,np)) #%% Hessian matrix
|
|
|
|
|
LL = self.nnlf(theta, data)
|
|
|
|
|
H = zeros((np, np)) #%% Hessian matrix
|
|
|
|
|
theta = tuple(theta)
|
|
|
|
|
for ix in xrange(np):
|
|
|
|
|
sparam = list(theta)
|
|
|
|
|
sparam[ix]= theta[ix]+delta
|
|
|
|
|
fp = self.nnlf(sparam,data)
|
|
|
|
|
sparam[ix] = theta[ix] + delta
|
|
|
|
|
fp = self.nnlf(sparam, data)
|
|
|
|
|
#fp = sum(myfun(x))
|
|
|
|
|
|
|
|
|
|
sparam[ix] = theta[ix]-delta
|
|
|
|
|
fm = self.nnlf(sparam,data)
|
|
|
|
|
sparam[ix] = theta[ix] - delta
|
|
|
|
|
fm = self.nnlf(sparam, data)
|
|
|
|
|
#fm = sum(myfun(x))
|
|
|
|
|
|
|
|
|
|
H[ix,ix] = (fp-2*LL+fm)/delta2
|
|
|
|
|
for iy in range(ix+1,np):
|
|
|
|
|
sparam[ix] = theta[ix]+delta
|
|
|
|
|
sparam[iy] = theta[iy]+delta
|
|
|
|
|
fpp = self.nnlf(sparam,data)
|
|
|
|
|
H[ix, ix] = (fp - 2 * LL + fm) / delta2
|
|
|
|
|
for iy in range(ix + 1, np):
|
|
|
|
|
sparam[ix] = theta[ix] + delta
|
|
|
|
|
sparam[iy] = theta[iy] + delta
|
|
|
|
|
fpp = self.nnlf(sparam, data)
|
|
|
|
|
#fpp = sum(myfun(x))
|
|
|
|
|
|
|
|
|
|
sparam[iy] = theta[iy]-delta
|
|
|
|
|
fpm = self.nnlf(sparam,data)
|
|
|
|
|
sparam[iy] = theta[iy] - delta
|
|
|
|
|
fpm = self.nnlf(sparam, data)
|
|
|
|
|
#fpm = sum(myfun(x))
|
|
|
|
|
|
|
|
|
|
sparam[ix] = theta[ix]-delta
|
|
|
|
|
fmm = self.nnlf(sparam,data)
|
|
|
|
|
sparam[ix] = theta[ix] - delta
|
|
|
|
|
fmm = self.nnlf(sparam, data)
|
|
|
|
|
#fmm = sum(myfun(x));
|
|
|
|
|
|
|
|
|
|
sparam[iy] = theta[iy]+delta
|
|
|
|
|
fmp = self.nnlf(sparam,data)
|
|
|
|
|
sparam[iy] = theta[iy] + delta
|
|
|
|
|
fmp = self.nnlf(sparam, data)
|
|
|
|
|
#fmp = sum(myfun(x))
|
|
|
|
|
H[ix,iy] = ((fpp+fmm)-(fmp+fpm))/(4.*delta2)
|
|
|
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|
H[iy,ix] = H[ix,iy]
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H[ix, iy] = ((fpp + fmm) - (fmp + fpm)) / (4. * delta2)
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H[iy, ix] = H[ix, iy]
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sparam[iy] = theta[iy];
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# invert the Hessian matrix (i.e. invert the observed information number)
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#pcov = -pinv(H);
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return -H
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if __name__=='__main__':
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#nbinom(10, 0.75).rvs(3)
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bernoulli(0.75).rvs(3)
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x = np.r_[5,10]
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npr = np.r_[9,9]
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bd0(x,npr)
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return - H
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def main():
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#nbinom(10, 0.75).rvs(3)
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import matplotlib
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matplotlib.interactive(True)
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t = _WAFODIST.bernoulli(0.75).rvs(3)
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x = np.r_[5, 10]
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npr = np.r_[9, 9]
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t2 = _WAFODIST.bd0(x, npr)
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#Examples MLE and better CI for phat.par[0]
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R = weibull_min.rvs(1, size=100);
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phat = weibull_min.fit(R,1,1,par_fix=[nan,0,nan])
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R = _WAFODIST.weibull_min.rvs(1, size=100);
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phat = _WAFODIST.weibull_min.fit(R, 1, 1, par_fix=[nan, 0, nan])
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Lp = phat.profile(i=0)
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Lp.plot()
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Lp.get_CI(alpha=0.1)
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R = 1./990
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R = 1. / 990
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x = phat.isf(R)
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# CI for x
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Lx = phat.profile(i=0,x=x)
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Lx = phat.profile(i=0, x=x)
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Lx.plot()
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Lx.get_CI(alpha=0.2)
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# CI for logSF=log(SF)
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Lpr = phat.profile(i=1,logSF=log(R),link = phat.dist.link)
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Lpr = phat.profile(i=1, logSF=log(R), link=phat.dist.link)
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Lpr.plot()
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Lpr.get_CI(alpha=0.075)
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dlaplace.stats(0.8,loc=0)
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dlaplace.stats(0.8, loc=0)
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# pass
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t = planck(0.51000000000000001)
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t.ppf(0.5)
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t = zipf(2)
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t.ppf(0.5)
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import pylab as plb
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rice.rvs(1)
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x = plb.linspace(-5,5)
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y = genpareto.cdf(x,0)
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_WAFODIST.rice.rvs(1)
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x = plb.linspace(-5, 5)
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y = _WAFODIST.genpareto.cdf(x, 0)
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#plb.plot(x,y)
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#plb.show()
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on = ones((2,3))
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r = genpareto.rvs(0,size=100)
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pht = genpareto.fit(r,1,par_fix=[0,0,nan])
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on = ones((2, 3))
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r = _WAFODIST.genpareto.rvs(0, size=100)
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pht = _WAFODIST.genpareto.fit(r, 1, par_fix=[0, 0, nan])
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lp = pht.profile()
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if __name__ == '__main__':
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main()
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Per.Andreas.Brodtkorb
15 years ago